"Input gain" has a range of null to extreme distortion, and is calibrated so at high noon the signal is passed with almost no waveshaping. The "gain control" knob and its associated jack allow modulation of the discrete VCA driving the wavefolding diode network. This allows the Wave Folder to be used as a VCA which can be very easily edged into distortion.

"Offset" feeds DC into the mix, which can act almost as a pulse width control for your distortion.

"Fold mix" is sort of a flavour control which controls the blend of the signal in a couple of different places in the circuit, and results in very wild waveshaping around 10 o'clock or so.